{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<center><strong>A Journey Into Math For Machine Learning</strong></center>\n",
    "<center><strong>机器学习之数学之旅</strong></center>\n",
    "<center><strong>之 逻辑回归(三)</strong></center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "这是**逻辑回归**的第三部分, 今天的主题下面第六部分, 通过梯度下降法找到最佳的模型参数, 如果你没有看上一节课的内容, 请在github项目根目录的readme文件里寻找链接.   \n",
    "**课程预览**:   \n",
    "(一). 二项逻辑回归的直觉;   \n",
    "(二). 逻辑回归的来历: $odds$和$probability$;      \n",
    "(三). 逻辑回归的计算: $logit$函数和$sigmoid$函数及它们的特性;   \n",
    "(四). 最大似然估计$(maximum \\ likelihood \\ estimation)$和损失函数;   \n",
    "(五). 困惑度$(perplexity)$的定义;   \n",
    "(六). 参数的获取: 梯度下降$(gradient \\ descent)$法优化参数;      \n",
    "\n",
    "**需要的组件**:   \n",
    "numpy, scikit-learn(数据集), matplotlib(可视化), plotly(可视化)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**(六). 参数的获取: 梯度下降 (𝑔𝑟𝑎𝑑𝑖𝑒𝑛𝑡 𝑑𝑒𝑠𝑐𝑒𝑛𝑡) 法优化参数**   \n",
    "1. 回顾我们在之前\"逻辑回归(一,二)\"中推导出的损失函数:   \n",
    "$$J(\\theta)=-\\sum_{i}^{m} Y log(\\hat{Y}) - (1-Y) log(1-\\hat{Y})$$\n",
    "上式中$i$是数据点序号, 一共$m$个数据点.\n",
    "2. 回顾我们在之前\"图解极大似然估计与3D可视化\"中画出的$log \\ likelihood$, 也就是我们现在损失函数的图像, 注意我们的损失函数是对原始的$log \\ likelihood$取负号, 使极大似然值的最大化问题变成最小化问题."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![title](./mle_convex.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "3. 我们看到上图, 损失函数是一个凸函数, 我们今天使用**梯度下降法**来寻找损失函数极小值, 或者说我们要求出, 当$\\theta$取什么值时, 损失函数可以到达极小值. \n",
    "4. 如果你不知道什么是梯度, 我来快速讲解一下, 看下图, 假设下图的函数是一个山坡, 我们现在站在函数表面某个点, 我们从这个点向上面看, 梯度指的是这个坡最陡峭的地方到底有多陡, 梯度下降指的就是沿着最陡的路径, 不断向下进行搜寻, 直到到达函数的最低点."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![title](./gradient.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "5. 比如说我们现在有一组参数$\\theta^T=\n",
    " \\left[\n",
    " \\begin{matrix}\n",
    "   bias & \\theta_1 & \\theta_2 \n",
    "  \\end{matrix}\n",
    "  \\right]$\n",
    "  和损失函数$J(\\theta)$, 我们想要知道这组参数$\\theta$取怎样的值时, 可以让$J(\\theta)$达到最小, 我们需要知道往哪个方向调节参数, 才可以让$J(\\theta)$变小, 我们这时就要求出梯度来, 我们要知道在当前点, 函数往哪个方向变化最陡峭, 然后往相反的方向, 也就是下山的方向搜寻, 期望最终能够达到最低点.\n",
    "6. 要求出梯度, 我们要求$J(\\theta)$对于$\\theta_j$的偏导数$\\frac{\\partial J(\\theta)}{\\partial \\theta_j}$, 偏导数的意义是, 它描述来函数在某一点的变化率, 说白了就是陡峭程度, 在这里可以这样理解, 我们稍微调节一点点$\\theta_j$, 会对$J(\\theta)$有多么大的影响, 而偏导数就是这个影响的比例, 或者说山越陡峭, 走一步而上升的海拔高度就越高, 而偏导数就是你走一步上升的海拔高度和步长的比例."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**求导过程**:   \n",
    "我们有损失函数$J(\\theta)=-\\sum_{i}^{m} Y log(\\hat{Y}) - (1-Y) log(1-\\hat{Y})$, 需要求$J(\\theta)$对于$\\theta_i$的导数$\\frac{\\partial J(\\theta)}{\\partial \\theta_i}$, 注意$\\hat{Y}=\\frac{1}{1+e^{-\\theta^T X}}$\n",
    "\n",
    "利用$\\frac{d}{dx} \\log_a(f(x)) = \\frac{1}{f(x)\\ln a} f^\\prime(x)$, 再将$\\hat{Y}=\\frac{1}{1+e^{-\\theta^T X}}$代入$\\log (\\hat{Y})$:\n",
    "\n",
    "$$\\frac{\\partial}{\\partial \\theta_j} \\log (\\hat{Y}) = \\frac{\\partial}{\\partial \\theta_i}\\log(\\frac{1}{1+e^{-\\theta^T x}}) \n",
    "=\\frac{\\partial}{\\partial \\theta_j}\\log(1)- \\log({1+e^{-\\theta^T x}})$$\n",
    "$$\\frac{\\partial}{\\partial \\theta_j} \\log (\\hat{Y})=\\frac{\\partial}{\\partial \\theta_j} - \\log({1+e^{-\\theta^T x}})=-\\frac{1}{1+e^{-\\theta^T x}} \\cdot e^{-\\theta^T x} \\cdot -x_j=(1-\\frac{1}{1+e^{-\\theta^T x}})x_j \\tag{eq.1}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "我们再来求$\\frac{\\partial}{\\partial \\theta_j} \\log (1-\\hat{Y})$\n",
    "$$\\frac{\\partial}{\\partial \\theta_j} \\log (1-\\hat{Y})=\n",
    "\\frac{\\partial}{\\partial \\theta_j} \\log(\\frac{e^{-\\theta^T x}}{1+e^{-\\theta^T x}})=\n",
    "\\frac{\\partial}{\\partial \\theta_j} -\\theta^T x- \\log (1+e^{-\\theta^T x})$$\n",
    "将$(eq.1)$代入上式求导:\n",
    "$$\\frac{\\partial}{\\partial \\theta_j} \\log (1-\\hat{Y})=-x_j+x_j(1-\\frac{1}{1+e^{-\\theta^T x}})\n",
    "= -\\frac{1}{1+e^{-\\theta^T x}}x_j \\tag{eq.2}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "我们将$(eq.1)$和$(eq.2)$求得的$\\frac{\\partial}{\\partial \\theta_j} \\log (\\hat{Y}) , \\quad\\frac{\\partial}{\\partial \\theta_j} \\log (1-\\hat{Y})$代入$\\frac{\\partial}{\\partial \\theta_j}J(\\theta)$, 注意$i$是数据点的序号$j$是特征的数量:\n",
    "$$X= \\left[\n",
    " \\begin{matrix}\n",
    "   x_{i=1,j=1}, \\ x_{i=2,j=1}, \\ ... \\ ,  x_{m,j=1}\\\\ \n",
    "   x_{i=1,j=2}, \\ x_{i=2,j=2}, \\ ... \\ , x_{m,j=2}\\\\ \n",
    "   x_{i=1,j=3}, \\ x_{i=2,j=3}, \\ ... \\ ,  x_{m,j=3}\\\\ \n",
    "  \\end{matrix}\n",
    "  \\right]$$\n",
    "$$\\frac{\\partial}{\\partial \\theta_j}J(\\theta)=\n",
    "-\\sum_{i}^{m}y_i x_{ij}(1-\\frac{1}{1+e^{-\\theta^T x_i}})-(1-y_i)x_{ij}\\frac{1}{1+e^{-\\theta^T x_i}}$$\n",
    "展开, 整理得到, 注意$\\hat{y}=\\frac{1}{1+e^{-\\theta^T x}}$:\n",
    "$$\\frac{\\partial}{\\partial \\theta_j}J(\\theta)=\n",
    "\\sum_{i}^{m}(\\frac{1}{1+e^{-\\theta^T x_i}}-y_i)x_{ij}\n",
    "=\\sum_{i}^{m}(\\hat{y}_i-y_i)x_{ij}\\tag{eq.3}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "我们还记得之前$\\theta$和$X$的向量表示形式\n",
    "$\\theta^T=\n",
    " \\left[\n",
    " \\begin{matrix}\n",
    "   bias & \\theta_1 & \\theta_2 \n",
    "  \\end{matrix}\n",
    "  \\right]\n",
    "\\quad\n",
    "X=\n",
    " \\left[\n",
    " \\begin{matrix}\n",
    "   1  \\\\\n",
    "   x_1  \\\\\n",
    "   x_2 \n",
    "  \\end{matrix}\n",
    "  \\right]$   \n",
    "我们发现$\\theta$里$bias$的对应着$X$里面的$1$, 由此可得出:\n",
    "$$\\frac{\\partial}{\\partial \\ bias}J(\\theta)=\n",
    "\\sum_{i}^{m}(\\hat{y}_i-y_i)\\tag{eq.4}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**搜寻下山过程**   \n",
    "我们现在已经得到了$\\theta_j$和$bias$的梯度, 我们用这个梯度来更新我们的参数, 我们定义一个学习率$\\eta$, 防止下山的时候跑的太快而跑过头, 一般学习率的取值都比较小, 在我们下面的实验中, 取学习率为$0.01$, 然后重复下面步骤, 直到收敛:\n",
    "$$\\theta_j \\gets \\theta_j - \\eta \\frac{\\partial}{\\partial \\theta_j}J(\\theta)\\tag{eq.5}$$\n",
    "$$bias \\gets bias - \\eta \\frac{\\partial}{\\partial \\ bias}J(\\theta)\\tag{eq.6}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 导入所需组件\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.colors import ListedColormap\n",
    "from sklearn.datasets import make_classification"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X (2, 100)\n",
      "y (1, 100)\n"
     ]
    }
   ],
   "source": [
    "X, y = make_classification(random_state=2)\n",
    "# 只取两个特征值, 二维特征值方便可视化\n",
    "X = X.T[:2, :]\n",
    "y = np.expand_dims(y, axis=0)\n",
    "print(\"X\", X.shape)\n",
    "print(\"y\", y.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 形成网格, 我们之后用来画分类边界\n",
    "interval = 0.2\n",
    "x_min, x_max = X[0, :].min() - .5, X[0, :].max() + .5\n",
    "y_min, y_max = X[1, :].min() - .5, X[1, :].max() + .5\n",
    "xx, yy = np.meshgrid(np.arange(x_min, x_max, interval),\n",
    "                     np.arange(y_min, y_max, interval))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 首先画一下数据点\n",
    "cm = plt.cm.RdBu\n",
    "cm_bright = ListedColormap(['#FF0000', '#0000FF'])\n",
    "plt.scatter(X[0, :], X[1, :], c=y.ravel(), cmap=cm_bright, edgecolors='k')\n",
    "plt.xlim(xx.min(), xx.max())\n",
    "plt.ylim(yy.min(), yy.max())\n",
    "plt.xlabel(\"theta_1\")\n",
    "plt.ylabel(\"theta_2\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sigmoid(z):\n",
    "    return 1 / (1 + np.exp(-z))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 初始化theta为全0\n",
    "theta = np.zeros([2, 1])\n",
    "# 初始化偏置为0\n",
    "bias = np.zeros([1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 进行正向计算并求出损失\n",
    "def forward(X, theta, bias):\n",
    "    z = np.dot(theta.T, X) + bias\n",
    "    y_hat = sigmoid(z)\n",
    "    return y_hat\n",
    "def compute_loss(y, y_hat):\n",
    "    e = 1e-8\n",
    "    return - y * np.log(y_hat + e) - (1 - y) * np.log(1 - y_hat + e)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 梯度下降, 参见(eq.3), (eq.4), (eq.5), (eq.6)\n",
    "def backward(X, y, y_hat, theta):\n",
    "    m = X.shape[-1]\n",
    "    # 求theta的梯度\n",
    "    delta_theta = np.dot(X, (y_hat-y).T) / m #(eq.3)(eq.5)\n",
    "    # 求bias的梯度\n",
    "    delta_bias = np.mean(y_hat-y) #(eq.4)(eq.6)\n",
    "    return delta_theta, delta_bias"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "step: 0 loss: 0.6931471605599454\n",
      "step: 100 loss: 0.3557057567504517\n",
      "step: 200 loss: 0.3290795009103417\n",
      "step: 300 loss: 0.32109595696394033\n",
      "step: 400 loss: 0.3178361588605987\n",
      "step: 500 loss: 0.31630155433263485\n",
      "step: 600 loss: 0.3155182426553739\n",
      "step: 700 loss: 0.31509745716547444\n",
      "step: 800 loss: 0.31486351407774793\n",
      "step: 900 loss: 0.31473027929320696\n"
     ]
    }
   ],
   "source": [
    "for i in range(1000):\n",
    "    # 正向\n",
    "    y_hat = forward(X, theta, bias)\n",
    "    # 计算损失\n",
    "    loss = np.mean(compute_loss(y, y_hat))\n",
    "    if i%100 == 0:\n",
    "        print(\"step:\",i,\"loss:\",loss)\n",
    "    # 梯度下降\n",
    "    delta_theta, delta_bias = backward(X, y, y_hat, theta)\n",
    "    # 更新参数\n",
    "    theta -= 0.1 * delta_theta\n",
    "    bias -= 0.1 * delta_bias"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 画等高线图\n",
    "data = np.c_[xx.ravel(), yy.ravel()].T\n",
    "# 计算出区域内每一个点的模型预测值\n",
    "Z = forward(data, theta, bias)\n",
    "Z = Z.reshape(xx.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 定义画布大小\n",
    "plt.figure(figsize=(10,8))\n",
    "# 画等高线\n",
    "plt.contourf(xx, yy, Z, 10, cmap=plt.cm.RdBu, alpha=.8)\n",
    "# 画轮廓\n",
    "contour = plt.contour(xx, yy, Z, 10, colors=\"k\", linewidths=.5)\n",
    "plt.scatter(X[0, :], X[1, :], c=y.ravel(), cmap=cm_bright, edgecolors='k')\n",
    "# 标出等高线对应的数值\n",
    "plt.clabel(contour, inline=True, fontsize=10)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
